NumberFoundation and Higher (some Higher only)

Standard form: GCSE maths practice with worked answers

Show Working has 3 kinds of standard form question for GCSE Maths, for Foundation and Higher (some Higher only). Every question is new each time and comes with the working, step by step.

Standard form writes very large and very small numbers as a number between 1 and 10 multiplied by a power of 10, such as 2 × 10⁵. You need to convert both ways, and on Higher, multiply and divide numbers in standard form.

Coming soon to the App Store

Worked example 1: write a number in standard form

Write 200,000 in standard form.

Standard form is a number from 1 up to (but not including) 10, multiplied by a power of 10.
Put the decimal point so there is just one non-zero digit in front of it: 2.
The point moved 5 places to the left, so the power of 10 is 5 (a big number has a positive power).
So the answer is 2 × 10⁵.

Answer 2 × 10⁵

01 / What's covered3 kinds of question

Standard form questions in the app

Each kind makes fresh questions every time, so you can practise as often as you like.

Write a number in standard formBoth tiers
Standard form to an ordinary numberBoth tiers
Multiply and divide in standard formHigher only

Worked example 2: multiply and divide in standard form

Work out (8.6 × 10⁹) ÷ (2 × 10²). Give your answer in standard form.

Divide the numbers at the front: 8.6 ÷ 2 = 4.3.
Subtract the powers of 10: 9 − 2 = 7.
So far: 4.3 × 10⁷.
Answer: 4.3 × 10⁷.

Answer 4.3 × 10⁷

A common mistake

Leaving the first number outside 1 to 10, for example writing 43 × 10⁶. In standard form that is 4.3 × 10⁷.

02 / Practise itiPhone and iPad

Practise standard form in Show Working

In the app, open Topics and choose Standard form for ten fresh questions. Ask for a hint if you are stuck, and open the working to see the method one step at a time.